Stretch heightmap over whole plane
You can do this also by hand, but one easy way would be  to use the import images as planes (included but not enabled by default), importing your "map".

You will get a plane with the same aspect ratio as your "map", of just 4 vertices, with the uv mapping already done. Just subdivide the plane 200 times (cuts, 6000/200=30), and apply displace modifier.

If using blender render, you can displace directly selecting the already imported "map" from the list. With cycles, the displace modifier only uses  a texture, but there is a button (see image below) in the modifier to "show the texture in the texture tab" where you can set the texture to image, and select your "map".

then in the modifier set it to use "uv coordinates"

cycles example:



blender render (internal) example: